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Uniformly $Hp$-stable Elements for the Elasticity Complex by Aznaran, Francis R. A.; Hu, Kaibo; Parker, Charles is a scholarly article available to read on EtoBox.

What is Uniformly $Hp$-stable Elements for the Elasticity Complex about?

For the discretization of symmetric, divergence-conforming stress tensors in continuum mechanics, we prove inf-sup stability bounds which are uniform in polynomial degree and mesh size for the Hu--Zhang finite element in two dimensions. This is achieved via an explicit construction of a bounded right inverse of the divergence operator, with the crucial component being the construction of bounded Poincar\'e operators for the stress elasticity complex which are polynomial-preserving, in the Bernstein--Gelfand--Gelfand framework of the finite element exterior calculus. We also construct $hp$-bounded projection operators satisfying a commuting diagram property and $hp$-stable Hodge decompositions. Numerical examples are provided.

Author

Aznaran, Francis R. A.; Hu, Kaibo; Parker, Charles

Published

2024

Language

EN